It should definitely check the HTML and CSS. It may not work well on sites that generate HTML from JavaScript though, but you can still check/validate a live DOM (see https://www.htmlvalidator.com/chrome.php ).

Have you tried using the trial version of CSS HTML Validator on your website? It should give you a great idea of how well it should work.

There's no specific configuration required for WordPress sites, but you can configure CSS HTML Validator as you wish (to your requirements).